The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs, except one. Find that odd number-pair.
(25, 200)
Finding the Odd Number-Pair Pattern
The question asks us to identify the number-pair among the given options that does not follow the same mathematical operation connecting the first number to the second number, as the other pairs do. We need to analyze each number-pair to find this common rule.
Analyzing the Number-Pairs
Let the first number in a pair be denoted by \(x\) and the second number by \(y\). We are looking for a relationship \(y = f(x)\) that holds true for most of the pairs.
The given number-pairs are:
- (24, 195)
- (26, 211)
- (25, 200)
- (36, 291)
Let's examine the relationship between the numbers in each pair.
Discovering the Mathematical Operation
Let's test the first pair (24, 195). We can see that 195 is roughly 8 times 24 (\(24 \times 8 = 192\)). The difference is \(195 - 192 = 3\). So, the operation could be multiplying the first number by 8 and then adding 3. Let's test this hypothesis: \(y = x \times 8 + 3\).
Testing the Operation on Each Pair
We will now apply the hypothesized operation \(y = x \times 8 + 3\) to the first number of each pair and compare the result with the given second number.
| Number-Pair (\(x\), \(y\)) | Operation \(x \times 8 + 3\) | Expected Second Number | Given Second Number | Follows Pattern? |
|---|---|---|---|---|
| (24, 195) | \(24 \times 8 + 3\) | \(192 + 3 = 195\) | 195 | Yes |
| (26, 211) | \(26 \times 8 + 3\) | \(208 + 3 = 211\) | 211 | Yes |
| (25, 200) | \(25 \times 8 + 3\) | \(200 + 3 = 203\) | 200 | No |
| (36, 291) | \(36 \times 8 + 3\) | \(288 + 3 = 291\) | 291 | Yes |
Identifying the Odd Pair
As shown in the table, the operation \(x \times 8 + 3\) correctly predicts the second number for the pairs (24, 195), (26, 211), and (36, 291). However, for the pair (25, 200), the operation \(25 \times 8 + 3\) results in 203, which is not the given second number (200).
Therefore, the number-pair (25, 200) is the one that does not follow the same mathematical operation as the others.
Conclusion
The odd number-pair is (25, 200) because the relationship between the numbers in this pair is different from the pattern \(y = x \times 8 + 3\) observed in the other pairs.
Revision Table: Number Pair Analysis
| Number-Pair | First Number (\(x\)) | Second Number (\(y\)) | Operation Applied (\(x \times 8 + 3\)) | Result | Pattern Match |
|---|---|---|---|---|---|
| (24, 195) | 24 | 195 | \(24 \times 8 + 3\) | 195 | Yes |
| (26, 211) | 26 | 211 | \(26 \times 8 + 3\) | 211 | Yes |
| (25, 200) | 25 | 200 | \(25 \times 8 + 3\) | 203 | No |
| (36, 291) | 36 | 291 | \(36 \times 8 + 3\) | 291 | Yes |
Additional Information on Number Series and Patterns
Finding patterns in number series or number-pairs is a common type of logical reasoning question. These questions test your ability to identify relationships between numbers based on mathematical operations.
Common types of patterns include:
- Arithmetic progressions (adding or subtracting a constant).
- Geometric progressions (multiplying or dividing by a constant).
- Operations involving squares or cubes of numbers (\(n^2\), \(n^3\)).
- Operations combining multiplication/division with addition/subtraction.
- Patterns based on prime numbers, composite numbers, etc.
- Patterns based on digits of the numbers.
To solve such problems, it's helpful to try basic operations first, look for differences or ratios between consecutive terms (or numbers in the pair), and test simple algebraic relationships like \(y = ax + b\) or \(y = ax^2 + b\).
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Important Questions from Number Based
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